^Q  A 

c?op.  Z 


/  . 


UC-NRLF 


^B    531    TTfl 


IN   MEMORIAM 
FLORIAN  CAJORl 


8061  '12  NVl  IVJ 

jiapuig 


Answers 


TO 


-EMENTARY  AlGEEEA 


DY 

FLORIAN  CAJORI 

AND 

LETITIA  ODELL 


Beat  pork 

THE  MACMILLAN  COMPANY 

1916 

A II  rights  reserved 


'     »^'  '.'., 


http://www.archive.org/details/answerstoeiementOOcajor 


Answers 


TO 


Elementary  ALd^EBRA 


BT 

FLORIAN  CAJORI 

AND 

LETITIA  ODELL 


THE  MACMILLAN  COMPANY 
1916 

All  rights  reserved 


•   .  •   •      •  * 


^ 


Copjrright,  1916 
By  The  Macmillan  Compant 


Set  up  and  eleotrotyped.    Publttbed  March,  1915 


CAJORl 


ANSWERS  TO  EXERCISES  AND  PROBLEMS 

IN  ELEMENTARY  ALGEBRA  BY 

CAJORI  AND  ODELL 

Page  3.-27.  22.  28.  14.  29.  27.  30.  121.  31.  29.  32.  4.  33.  25 
34.  2V4.  35.  64.  36.  964.  37.  47.  38.  10.  39.  259.  40.  111.  41.  42. 
42.  75.  43.  75.  44.  70. 

Page  6.— 1.  17.  2.  98  lbs.  3.  467*  mi.  per  hr.  4.  46  mi.  per  hr. 
5.  20  hrs.  6.  33  ft.  8.  45,  30.  9.  80,  46.  10.  $30,  $6.  11.  $84,  $12. 
12.  $80,  $44.  13.  5.  14.  IVa  oz.  15.  1184.  16.  7.  17.  $6000,  1"; 
$5000,  2";  $3000,  3".  18.  $12,000,  A^s;  $4000,  B^s;  $8000,  C's.  19.  9  oz. 
20.  20.  21.  1.20  ft.  22.  19.71.  23.  6.674;  4.626. 

Page  10.— 16.  (1)  32.  (2)  64.  (3)  96.  (4)  896.  (5)  35.  (6)  246. 
(7)243.  (8)73,255.  (9)3.  (10)1.  (11)1.  (12)6234.  (13)139.  (14)59. 
(15)  243.  17.  4;  64;  2500;  5184;  1024;  324;  40,000.  18.  80;  970; 
9960;  99,950.   19.  V4;  Va;  2;  "A;  "/le.   20.  0;  0. 

Page  12.— 1.  17.  2.  137.  3.  18.  4.  21.  5.  24.  6.  50.  7.  70. 
8.  0.   9.  240. 

Page  13.-1.  0.  2.  10.  3.  27.  4.  93.  S.  3.  6.  24.  7.  8.  8.  4. 

Page  13.-1.  V«.  2.  2.  3.  589.  4.  V4.  5.  6V11.  6.  2V20.  7.  156. 
8.  56.    9.  82.      10.  4.      11.  Yes;  No.      12.  No;  No. 

Page  18.— 4.  -  10.  5.  45.  6.  15.  7.  -  70.  8.  80.  9.  -  4. 
10.45.  11.75;  -45.  12.-20.  13.-10.  14.10.  15.-40. 
16.  80.  17.  70.  18.  -  65.  19.  -  70.  20.  -  20.  21.  -  45.  22.  -  2. 
23.  20.    24.  -  80.    25.  -  95.    26.  -  95. 

Pages  20-22.— 1:  $100.  2.  $180.  3.  5  cts.  4.  19  ft.  lower. 
5.  8  in.  higher.  6.  92  mi.  7.  38**  above;  12^  belaw;  112°  below;  162^ 
below;  222°  below.     8.  8000  ft.  higher;  1000  ft.  lower;  5600  ft.  lower; 

.   6900    ft.    lower;    6100    ft.    lower.      9.  51V7^      10.  -  PA^      H.  $140. 

>  12.  33°  11'  30".  13.  1°  48'  30".  14.  3'  32V2".  16.  43850'.  17.  3  hrs. 
18.  10  mi.  per  hr.     19.  249  lbs.  upward. 

Page  24.— 1.  14  daa.      2.  46  ft.,  1840  cu.  ft. 

Page  25.— 1.  11.  2.  14.  3.  -  48V7.  4.  -  351.  5.  3.  6.  76iVi4. 
7.  12.    8.  -  22.     9.  67. 

3 


915799 


4  ANSWERS. 

Pages   26-27.— 1.  15o.         2.  -  3c.         3.  5x  +  12y  +  5z.         4.  6a;. 

5.  14a;  +  lOy,  6.  15c  -  6d  +  39c.  7.  -  8a  +  356  +  4e. 

8.  14(a  +  6).  9.  -  7a^h^  -  2a¥  +  7ab^c.  10.  9fg  -  Sgh, 
11.  5a  H-  9b  +  10c.      12.  -  9aa;.      13.  3mn.      14.  -  18A;Z.      15.  -  5ac 

-  36c  -  9cdJ.     16.  55s^  -  9ty,     17.  10a  -  x. 

Pages  27-28.— 1.  lloc^  +  362c  -  Gc^  +  7ac.  2.  3a2  +  962  +  3^2. 

3.  22a;  -  2/  +  5xy.        4.  12a;  -  7?/  -  142  +  7w  "  Sv.        5.  4a  -  6  +  6c. 

6.  5a  +  86  +  4c.    7.  2a  +  36  +  14c  -  6rf  +  3/.   8.  4a«6  +  lla63  -  lla6. 

9.  -  a  -  26  +  5c  +  d  +  4e.  10.  7a;  +  ISy  -  132  +  5w  +  v. 
11.  -  7a;  +  2!/  +  62.  12.  2a  -  4d.  13.  -  3m  +  16n  +  6p. 
14.  -  1?/  4-  6(7  +  47^.         15.  36  +  2c  -  lid  +  3e.         16.   -  17a  -  14r 

-  22s.  17.  5a  -  286  -  c.  18.  4x  +  2/  +  z  +  5ii;  -  a  +  6  -  6c  +  4d, 
19.  _  2a  -  26  -  30c.  20.  -  4a  +  216  +  31c.  21.  4a*  -  8a. 
22.  6,  -  6,  3,  12,  -  12,  -  9,  9,  -  10.  23.  4,  20,  21.  24.  4,  9,  1,  100,  36. 
25.  -  60,  120,  +  180,  -  60,  -  600.  26.  -  8,  -  27,  -  1,  1000,  216, 
8,  -  1000.      27.  -  4,  4000,  -  3000,  -  1000,  1000. 

Page  29.-2.  3a;2  -  4a;  -  y.  3.  3a;2  +  5a;  -  Wy,  4.  a;^  -  2a?  -  15y. 
5.  5a2  +  5a  -  26.  6.  5a2  +  a  -  6.  7.  ~  7a2  +  29a  +  146. 

8.  3a3  +  562.      9.  5^3  +  263.       10.  -  a^  -  46*. 

Pages  30-31.— 1.  4a  +  5  -  4c.         2.  -  2c  -  Sd.        3.  a  +  36  +  3c. 

4.  -  a  +  6  -  7c.     5.  -  4n.     6.  3(f  -  7e  -  2/  +  6^^.     7.  -  162  +  12m 

-  n  -  3r  -  5<  +  92/.  8.  14a;  +  Qy  +  w.  9.  -  14a  +  56.  10.  -  4r. 
11.  6c  -  4d  -  6  +  3/.  12.  4a  -  26  -  c  +  4d  +  c.  13.  4a  +  26  -  2c. 
14.  -  4a  +  36  -  5c.     15.  6n.     16.  -  llw  -  2n  +  4p. 

Pages  31-32. — 1.  x  +  (a  +  h  —  c  +  d)  -\- y  +  i"  m  +  n  —  s),    2.  2a; 

-  (~  3a  +  46  -  5c)  -  ^  -  (6/c  -  8Z  -  7/  +  4g).  3.  (3a  +  2w?  -  3c) 
+  a;  +  (~  4r  +  50  +  2/  +  (5^  -  6w?  +  7i)  -  a;  4-  (a  +  6).  4.  -  (9m 

-  8i  +  7w)  +  62/  -  (-  5i  +  4r  -  3e)  +  a;^  -  (-  2w  -  3a).  5.  Sy  + 
(-  c  +  3a)  -  2a;  +  (46  -  2d).                6.  -  (56)  -  a;  +  31/  -  (4c  -  5d). 

7.  (-  5m  +  6n)  +  7x  +  (-  3p)  -  42/.        8.  Sy  -  (3c  -  26  +  5a)  +  5a;. 

Page   36.— 1.  4.     2.  5.     3.  -  2.     4.  6.     5.  6V2.     6.  -  5.      7.  72/3. 

8.  -  IV3.  9.  2.  10.  -  20.  11.  Vs.  12.  -  60.  13.  (a  -  6)/2. 
14.  a  -  6  -.  c.  15.  (c  -  6)/2a.  16.  (a  +  6)/6.  17.  a  -  6.  18.  1/a. 
19.  13.      20.  (3c  -  26)/a. 

Page  37.— 1.  -  22.    2.  P/e.    3.  -  "/s.     4.  27V3.     5.  60.     6.  4. 

Pages  37-40.— 1.  18  ft.;  8  ft.  2.  70  -  2w;;  (70  -  1)12.  3.  180  ft.; 
60  ft.  4.  70  yds.  5.  70  lbs.;  30  lbs.  6.  25V7  lbs.  7.  66Vs  lbs.;  33 Vs  lbs. 
8.  126;  80.  9.  258;  -  42.  10.  I2V2;  -  I2V2.  H.  20;  -  4. 
13.  22  min.     14.  SVa  min.        IS.  8  dimes;  11  nickels.        16.  9  dimes; 


ANSWERS.  5 

7  quarters.  17.  24  nickels;  79  pennies.  18.  7  dimes;  7  quarters. 

19.  45°;  -  10^  20.  48°.  21.  $437272.  22.  $1500  at  6%;  $1200  at  5%. 
23.  $3000  at  6%;  $2000  at  7%.  24.  James  54  words;  John  108  words. 
25.46;    35.  26.  3a/2;    (5a  +  26)/2.         27.  (a  +  6)/2;    (a  -  6)/2. 

28.  c/2;  ~  c/2.  29.  a  dimes;  b  quarters.  30.  2T  +  t.  31.  (3D  +  d)/2. 
32.  Father  $4a/5;  son  $a/5.  33.  (p  +  2(?)/4;  (p  -  25)/4.  34.  P/8;  3P/8. 
35.  12;  13.     36.  24,  25,  26.     37.  (s  -  3)/3;  s/3;  (s  +  3)/3.     38.  50;  52. 

Pages  42-43.— 1.  6a^y  +  Sexy^  +  ISxyz  -  15t^X2/.      2.  lOa^fec  -  20ah^c 
+  10a6c2e  -  40abcd  -  lOahce.  3.  Ox^j/^z^  +  3Qxyh^  -  45x^2/323  - 

ISx^y^z,  4.  -  6mn'o2  -  lOn^o^  -  Sn^o^  +  lOn^o^p.  5.  -  35  +  14o 
-  146  +  21c  -  28e.  6.  -  4m  +  lOn^  +  120  -  lOp.  7.  ^aJ^hcd  - 


^ux 


.3 


4ab^cd  -  8a6c*d  -  12ahcd*,  8.  -  ISafea;^  -  Qax*  +  16a<ix'  -  2a/i 

+  2agx\  9.  12a  -  186  -  24c  -|-  SOd,  10.  -  10a;  +  5qy  -  152. 

11.  72. 

Pages  45^6.-1.  x^  +  3a;  +  2.  2.  2a;«  +  7a;  +  3.  3.  2a^  -  7x  +  3. 
4.  5x3  4.  21x2  +  6a;  +  8.  5.  -  Oa;^  +  20x2  -  4x  -  6.  6.  2/*  -  7y^ 
+  10^  +  42/  -  20.  7.  2/«  -  2/5  -  ^<  -  2/2  +  2/  +  1.  8.  2^  -  ^2  «  -^ 
+  1.       9.  y*  -  7y^  +  132/^  -  16^  +  5.       10.  -  22^  -  22'  +  I222  -  2O2 

-  60.  11.  6x6  _  9a;3  4.  15a.  ^  2x*y  -  3x22/  +  St/.  12.  5x«  +  9x» 
+  6x2  4  2x.  13.  626  -  422^  -  22  4  7.  14.  2x3  4.  2^2  -  3x  +  2. 
15.  x3  -  V3X2  4.  10/33.  _  1.            15.  26  _  1,            17.  33.3  _  a;2  _  63.  4  4^ 

18.  -  2«  +  8z3  -  1922  +  82  +  12.  19.  -  32/5  +  15y^  +  IQy^  +  lly^  + 
7y  -  6.      20.  8x«  +  lOx^  -  x^  -  24x3  -  9x2  4.  6x  +  10.      21.  2x«  +  5x« 

-  7x<  -  9x3  4.  5a;2  -  8x  4-  12.  22.  15x2  -  xy  +  2x2  +  15x  -  2y^  -  3^2 
+  52/  -  2*  +  52.  23.  2a2  +  ac  -  262  4.  55^  -  3c2.  24.  x*  +  x^y  +  2x3 
4-  2x22/  -  2x22/2  +  2x2/2  +  x2  +  xy,  25.  x3  +  x^y  +  x2/2  +  x22  +  X22  + 
2/3  +  y^z  +  2/2^  +  2^-       26.  a2  -  2a6  +  6a/  -  4a^  +  e2  -  6e/  +  4e^  +  9/2 

-  12fg  +  4^2.  27.  a2  +  2a6  -  2ac  +  2ad  +  2ae  +  62  -  26c  +  2bd  + 
26e  +  c2  -  2c(i  -  2ce  +  J2  +  2c?6  -f  eK  28.  a*  +  2a36  -  2a262  -  2a63 
+  6*.     29.  x3  -  6x2?/  -I-  12x2/2  -  SyK     30.  x3  -  Sx^y  +  3x2/2  -  y^  +  Sx^z 

-  6x^2  +  Sy^z  +  3x22  _  3^,22  +  23.  31.  a3  -  3a26  +  3a62  _  53  _  3^2^ 
4-  6a6c  -  362c  +  3ac2  «.  35^2  -  c\ 

Pages  46-47.-2.  -  5.     3.  -  Vs.     4.  -  Vt.     S.  -  'A.     6.  5.     7.  11. 

8.  -  5.  9.  -  13.  10.  -  5.  11.  2/6.  12.  -  2.  13.  V19.  14.  Vu. 
15.  -  «V6.     16.  -  V2.     17.  -  Vi4.     18.  -  7.     19.  5.    20.  Vs. 

^n      i     -31a368c-2                 ^    --  5x^2^                 ,    69m3n-3o-« 
Page  50.~1.  ^ .  2.  — g — .  3.  g . 

A    -  56"2c-i(^'4g3  -  pr2  18c8  ^   16?«m^         .   .    . . 

4.  g .      5.-2^.      ^'ZrmH^'      ^•■49i;r-      8.  7aft. 

9.  IV/sxyin.      10.  143/5  nV  in.      11.  Z^I^-^cH.      12.  25x22/'. 


ANSWERS. 


Page  51.-1.  ~. 


2. 


17at*w 
12     • 


4. 


7. 


12 


-5c» 


8. 


3M 


c*y^2' 


4a2e= 

30;t*t^to^ 
7xy^z 

Page  53.— 1. 


X 

3w;      * 


13. 

5d^y 
2ax  ' 


14. 


10. 

3no»     ' 


5   ^' 
11. 


'    21m   • 
~  16a^b^c*dh 
f9 


Sa^dehH^ 


7mo^ 


-  117dg*x*yh 
124fh* 


•       h^cy      '  -2QkH*p' 

Page  54.— 1.  4x  -  32^.        2.  4a  +  2.        3.  3  -  4m.        4.  be  -  4(f/3. 

5.  1  +  2/ii.  6.  2  -  xz'.  7.  3a;V2  ~  2/*  4-  2.  8.  3r  +  4  ~  2/r. 
9.  4/3^»  -  5/3xy  -  4/3.        10.  3/4  +  5zV4  +  7wj/4.        11.  5  +  6ac  -  8a. 

12.  -  c  +  4e/d  -  ce2.    13.  ~  5/3  +  2xy  -  yK    14.  -  3/2  +  ab^  -  2(ib^c\ 
Page  56.— 1.  a;  +  1.     2.  y  +  2.     3.  x  +  2.     4.  2  -  2.     5.  a;^  -  a;  +  1. 

6.  w^  -w  +  h      8.  c2  +  c  +  1.      8.  x^  +  2x^  +  4x  +  8.      9.  6x^  +  7x« 
-Sx  +  30.    10.  5x3  _  ga;2  4.  9^  4.  2.     IIZ  2/*  -  y'  -  2/  +  1.     12.  a  +  6 

13.  X  —  y.     14.  X  +  y-     15.  X  —  y,     16.  m^  —  mn  -^  n^.     17.  m*  -f  mn 
*  +  nK  18.  x*  +  x'2/  +  x^y^  +  X2/'  +  y*,  19.  a^  4-  a'b^  +  b*, 

20.  c'  +  dK         21.  a^  -  b».         22.  x^  +  x*y  +  a;V  +  x^y'  +  a;?/*  -f  y^ 
23. 


x*  —  x^y  +  a;22/2  —  x?/^  +  2/*. 


949 


Page  57.-1.  x^  +  llx  -f  106  +  ~^£^  .      2.  2/^  -  42/  +  1  +  ^^. 

4.  w«  -  w«  +  tr»  -  1  +  ■     ^ 


28  +  4z2 


M- 


-212  +  5 


22—42 

3a2  +  16a  -  10 


7.  r 


12  , 


a^  -7 
r8  +  H  -  1  + 


6*  m'  —  5m 


uj2-f  1  • 
Q   ,    -  m*  +  9m  +  16 


r*  +  l' 


8.  «"  -H  2s«  +  45  + 


8g  ~  1 
fi''  ~2  ' 


-  SVt.     S.  -  7.  6.  -  14. 

11.  3(c  -  d)/4.  12.  am/n. 

16.  -  5V7.  17.  -  14. 

21.  5r5/34. 


Page  59.-1.  46.     2.  3IV3.  3.  2V3.     4. 

7.  3o.        8.  3mn.        9.  2c.  10.  I2V2. 

13.  mi/20.  14.  rs/-  6.  15.  3IV3. 

18.  -  3.125  mn.     19.  13Vio7.  20.  am/-  n. 

Pages  60-63.— 4.  92;  115.  5.  -75;   -200.  6.  62;   -279. 

7.  -  38;  95.  8.  $300;  $350.  9.  $4480.  10.  7  yrs.  V2  mo.  11.  120  ft. 
12.  180  ft.  14.  15,750  ft.  15.  I28V7  cu.  ft.  cement;  2577?  cu.  ft.  sand; 
5UV7  cu.  ft.  gravel.  16.  26Vi7  cu.  ft.  cement;  66 Vn  cu.  ft.  sand;  132 Vn 
cu.  ft.  gravel.  17.  A,  $20777;  B,  $36272;  C,  $155Vi4.  18.  16. 

19.  Tea,  75c;  Coffee,  50c;  Butter,  30c. 

Page  65.-2.  16?.    .3.  Between  11  A.M.  and  Noon.     4.  18^ 

Pages  72-76.-1.  2Vii  Kg.,  37ii  Kg.,  47ii  Kg;  46.2  lbs.,  37.4  lbs.; 
28.6  lbs.     2.  12.1  yds.,  9.35  yds.,  7.15  yds.,  4.4  yds.      5.  86**  F.,  77**  F., 


ANSWERS.  7 

62V6'*  F.,  32**  F.,  14**  F.,  -  4**  F.  6.  262/8**  C,  I8V3**  C,  IIV9**  C,  0^  C, 
-  9V»**  C,  -  13V3**  C,  -  im  C,  -  19V»^  C.  8.  $8V8,  SUVs,  S14Ve, 
$20,  $23 Vs,  S26V8.  9.  S6,  $18,  $24,  $27V6,  $30.  11,  $10.64,  $15.80, 
$26.35,  $39.52.     12.  $94,875,  $75.90,  $28.46. 

Pages  77-78.— 1.  12.  2.  1.  3.  Vs.  4.  24.  5.  14.  6.  1.  7.  12. 
8.  6.     9.  3.     10.  10.     11.  2.     12.  5.     13.  6.  .  14.  3.     IS.  41.     16.  V2. 

17.  18.     18.  6.     19.  3.    20.  5. 

Pages  78-83.— 1.  24.       2.  14,   15.       3.  9,   15.       4.  45,  3.       5.  7. 

6.  15  in.,  20  in.  7.  108  sq.  in.  8.  7  ft.,  2  ft.  9.  36  sq.  ft.  10.  25,  26. 
11.  24,  26,  28.  12.  15,  16,  17;  3  times;  yes.  13.  22,  24,  25,  26. 
14.  15  yrs.        15.  50  jrrs.,  25  yrs.        16.  42  yrs.        17.  45  yrs.,  15  yrs. 

18.  15  yrs.  19.  $150.  20.  50,  2c;  75,  Ic.  21.  46V3  mi.  by  trolley; 
68V8  mi.  by  train.  22.  7,  5c;  5,  25c.  23.  12  quarters,  15  halves. 
24.  2  nickels,  16  quarters,  12  dimes.  25.  1",  60;  2",  50;  3",  40.  26.  15. 
27.  500  mi.  28.  21  mi.  29.  $4800.  30.  $6550.  31.  4V2  yrs.  32.  4%. 
33.  $5800.  34.  $400.  35.  $3000  @  51/2%;  $680  @  6%.  36.  9V2  mills. 
37.  8V2  mills.  38.  6V4  mills.  39.  6V2  mills.  40.  VU  mills. 
41.  VU  mills.  42.  7V2  mills.  43.  $7353.54.  44.  $3005.05. 
45.  $9747.74.  46.  ^30,050.51.  47.  $17,570.  48.  17,545. 
49.  $22,000.  50.  $34,000.  51.  $45,500.  52.  $52,000.  53.  3V2  doz. 
54.  9  hrs.,  90  mi.,  108  mi.  55.  3600.  56.  8.4  in.  57.  88V2  mi. 
58.  144  sq.  yd. 

Pages  93-94.-1.  4(a  -  2).  2.  x\l  -  x),  3.  3a(6  -  2c). 

4.  2x2(2/  -  3z).  5.  a\h  +  c  -  d).  6.  2mhi{l  -  3n  +  4n2). 

7.  5aH3a2  -  2a  -  5).  8.  8c2(2c  +  d  -  8c*d2).  9.  ^{^  ^  ^ -\- x^  ■\-  x^). 
10.  6aS(2a~  4a2  +  1).  11.  x{x  +  22/-1  -  z).  12.  9dK2d^-  9d«+  3  -  d). 
13.  17aH2/*  -  2a2/'»  +  4).  14.  Zxyz{x  +  2/  +  2).  15.  llmK^n^  -  5n  +  6r). 
16.  a^h^c\ab  -  ac  ■\-  he),  17.  2bcHK^  -f  4d  -  6c).  18.  hgh(15h^h 
+  Ugh  -bg  -  6).              19.  a"(6  -  c  -  d).           20.  2aj«(l  -  36  +  4c). 

21.  3a«6»c(l  -  3(i  +  2e).  22.  y^^(c  -  d  +  g).  23.  6a*6»(l  +  2a  -  Za^), 
24.  22/*(4x»  -  2  -  x«2«). 

Page  95.— 1.  {x  -  y){a  +  h).  2.  (x  +  2y){a  -  &).  3.  (c  -  aXx  +  y), 
4.  (c  -  d)&  -  2).  5.  (3c  +  d){a  -  6  -f  c).  6.  (a  +  x)(-  2  +  a  -  e). 
7.  (a  -  c)(6S-  c).  8.  (x  -  2/)(r  +  s  -  0-  9.  (x  -  2/)(a  -  6). 

10.  (a;  -  2/)(3  -  d).  11.  (c  +  d){a  ~  6).  12.  (1/  -  b)(x  -  a). 

13.  (d  -f  3)(c  -  2).  14.  (3s  +  2)(2r  -  3).  15.  (y  +  l)(y^  +  1). 

16.  (a  -  l)(a  +  6).      17.  (x  -  2i/)(66  +  25c).      18.  fe(3  -  5y^)(l  -  2y), 

19.  (7r  -  20(7o  +  36).      20.  (1  +  a)(l  -f  6).      21.  (a  +  b)(x  +  y -^  z). 

22.  (x  -  l)(a  -  6  -  c).        23.  (i  -  y)(a  +  26  +  c).        24.  (a  -  6  -{-  c) 
'  (2  +  X  +  y).  -. 


8  ANSWERS. 

Page  96.— 1.  (m  +  n)K     2.  (o«  -  2b)2.     3.  (a*  -  Sb*)*.     4.  (x  4-  12)2. 
5.  (63  +  4)2.    6.  y  +  8)2.    7.  (2/  -  Va)*.    8.  (VsX  +  1/4)2.    9.  (6a  -  6«)2. 

10.  (lie*  -  62).  11.  (Sy  4.  1)2.  12.  (10  +  hy.  (13.  (3u?  -  3)2. 
14.  (1  -  136)2.  15.  (5  +  4a)2.  16.  (3c  +  9^^68)2.  17.  (4n  -  7p)2. 
18.  {151  -  42/)2.  IP.  (2m  +  16w)2.  20.  (15s  -  2^*^)2.  21.  (a-\'h-  3)2. 
22.  [{x  -  yy  +  4]2.        23.  [6(r  -  s)  -  5]K        24.  [3(a  +  6)  -  (c  +  d)]2. 

25.  [2  -  3(a  -  x)]K  26.  (x  +  1/  -  2)2.  27.  {c  +  d  +  e)K 
28.  (a  -  6  +  2)2.      29.  (2w  -f  n  +  1)2.      30.  (g  +  3/i  +  1)2. 

Page  97.-— 1.  {x  +  y){x  -  y),     2.  (a  +  3)(a  -  3).     3.  (1  -|-  6)(1  -  6). 
4.  (2  -f  m2)(2  -  m2).  5.  (2/»  -|-  5)(2/»  -  5).  6.  (8c  +  z)(8c  -  z). 

7.  (5c3  +  7d2)(5c8  -  7^2).  8.  (9  +  lla;«)(9  -  llx»). 

9.  (3r  +  40 (3r  -  40-  10.  (lOpg  +  9w^)(10p?  -  9i^). 

11.  (6x5  +  72/6) (6x8  -  72/6).  12.  (12w;  +  bx^){\2w  +  5a;2). 
13.  {h  4-  13) (A  -  13).  14.  (2a  +  l)(2a  -  1).  15.  (4a6  +  5c)(4a6  -  5c). 
16.  (15?  +  122) (15g  -  122).  17.  {lOw  +  16t;2)(10w;  -  16i;2). 
18.  (3x2/  +  ll)(3a;2/  -  11).  19.  (7c3  +  8<*)(7c»  -  8^*). 
20.  (17a6c  +  5(i)(17a6c  -  5d).  21.  {x -^  y  ■\- l){x -^  y  -  1). 
22.  (a  4-  36  +  c){a  +  36  -  c).  23.  {x  -  2y -\-  z){x  ~  2?/  -  2). 
24.  (m  +  6w  +  2r)(m  +  6n  -  2r).            25.  (7d  -  r  +  5s)(7(i  -  r  -  5s). 

26.  (a  +  6  +  2c)(a  +  6  ~  2c).  27.  (x  -  y  -\-  z){x  -  y  -  z). 
28.  (c  -  3d  +  e)(c  -  3rf  -  e).  29.  (6  -  9  +  7s)(6  -  9  -  75). 
30.  ((i  -  6  +  5t)(d  -  6  -  50.  31.  (1  +  o  4-  6)(1  -  a  -  6). 
32.  (4  +  a;  -  2/)(4  -  x  +  j/).  33.  (3  +  m  -  3n)(3  -  m  +  3n). 
34.  (fc  +  A  4-  10)(A;  -h"  10).  35.  (a  4-  6  4-  c){a  -  6  -  c). 
36.  (i  +  m  -  n)(«  -  m  +  n).  37.  (7  4-  c  4-  3(i)(7  -  c  -  3d). 
38.  (9p  4-  6g  -  l)(9p  -  6g  4-  1).  39.  (10s  4-  4/i  4-  2) (10s  -  4h  -  2). 
41.  (x  4-  22/  4-  w  -  n)(x  4"  22/  -  m  4-  w).  42.  (3c  -  3d  4-  2x  -  22/) 
(3c-  3d  -  2x  +  22/).  43.  (8^1  4"  8Z  4-  7r  -  7t){Sh  4-  8Z  -  7r  4-  70- 
44.  (12m  -  12x  4"  Hw  4-  ny){12m  -  12x  -  llw  -  lly),  45.  (62/-  62 
4-  Uw  4-  14x)(62/  -  62  -  Uw  -  14x).  46.  (c  +  d  +  m  -  r){c  4-  d 
—  m  4-  0« 

Pages    lOO-lOl.-l.  (3x  4-  2)(2x  +  1).  2.  (3x  4-  5)(2x  4-  1). 

5.  (3x  +  l)(x4-2). 
8.  (8m  -  15)  (m  -  2). 
11.  &  -  2){2t  -  5). 
14.  (62/  +  5)(5y-l). 
17.  (5m  -  2)  (3m  4-  4). 
20.  (3d  +  l)(2d  -  5). 
23.  (3o  -  6) (a  4-  46). 


3.  (12x  -  5)(x  4-  1). 

4.  (7x  +  4)(x4-l). 

6.  (5x4-7)(4x4-l). 

7.  (2a  -  l)(a  -  13). 

9.  (56 -6)  (26 -5) 

10.  (32/  -  5) (22/  -  7). 

12.  (3s  -  2)(s  4-  5). 

13.  (8s  4- 3)  (3s -1). 

15.  (4m  4- 3) (2m  -7). 

16.  (3m  +  2)(m  -  1). 

18.  (6a-  l)(3a  +  2). 

19.  (6c  -  l)(c-f  6). 

21.  (11^  4-  i)(g  ~  2). 

22.  (2^4-5A)(y4-3/i). 

24.  (3a4-26)(a-36). 

ANSWERS.  9 

Page  101.— 1.  ix  +  y){z^  -  xy -{-  y^).  2.  (a;  -  2/)(x«  +  xy  +  y% 

3.  (m  +  l)(m2  -  m  +  1).  4.  (m  -  l)(m2  +  m  +  1). 
5.  {ab  +  2)(a262  -  2a6  +  4).  6.  {cd  -  3)(c2d2  +  3cd  +  9). 
7.  (4a  -  l)(16a2  +  4a  +  1).  8.  (56  +  6) (2562  -  306  +  36). 

9.  {2g  -  36) (4^2  ^  Qgh  +  g/^i),  iq.  (xy  +  7)(xV  -  7^2/  +  49). 
11.  {x^  +  2/')(x*  -  xV  +  2/0.  12.  (2a«  -  62)(4a*  +  2a262  +  6*). 
13.  (1  -  3a3)(l  +  3a»  +  9a«).  14.  {m*  +  n*){m^  -  m*n*  +  w«). 
15.  (3c«  +  l)(9cio  -  Sc^  +  1).  16.  (2a'*  -  l)(4a«»  +  2a»  +  1). 
17.  (6«'»  +  c2")(6«'»  -  63«c2»  +  c*«).  18.  (x  +  y)(x^  -  xy  +  y^){x^  - 
xV  +  2/').  19.  (4a  -  56)(16a2  +  20a6  +  256^).  20.  27(2  -  x«)(4  + 
2x8  4.  a.12). 

Pages   102-103.— 1.  a{a  +  1)K  2.  2(x2  +  3)2.        3.  y*{S  -  ^y^)K 

4.  6(6  +  1)(6  -  1).  5.  (x2  +  4)(x  +  2)(x  -  2).  6.  (a  +^7) (a  ~  1). 
7.  (a  +  15)(a  +  1).        8.  (x  -  y)ia  -  2).        9.  (w  -  n)ia  +  6)(a  -  6). 

10.  (c  +  DHc  -  1).  11.  (x^  -  7)(x  +  l)(x2  -  X  +  1).  12.  (fc2  -  8) 
(fc  +  3)(/b  -  3).  13.  (2  +  x)(4  -  2x  +  x2)(2  -  x)(4  +  2x  +  x*).  14. 
{h  -  7)(A2  -  2).  15.  (9^12  +  ]^2)(^h  +  /^)(3;i  _  /;).  15.  (^j  _  ^Z  +  2) 
(x  -  2/  -  z).         17.  (3m2  +  7)(m2  -  5).         18.  (y  -  4)(2/2  +  42/  +  16). 

19.  (L  +  1/2)^  20.  (x  +  2)2(x  +  2).  21.  (a  +  6)». 
22.  2(a  -  7)(a2  -  5).  23.  (a  +  6  +  1)2.  24.  (a  -  6  +  3)(a  -  6  -  3). 
25.  (c  +  a-6)(c-a  +  6).  26.  (1  +  xO(l  -  x*  +  x*). 
27.  (r  +  14)(r  -  11).  28.  (x  +  21)(x  -  10).  29.  (a2  +  62)(a*  -  a262 
+  h*)(a  +  6)(a2  -  06  +  62)(a  -  6)(a2  +  a6  +  6*).  30.  (2s  -  l)(s  -  2). 
31.  7(a  -  5)2.  32.  6(3  +  2x)(l  -  x).  33.  (17w?  -  9)(w?  +  2). 
34.  (3x»  +  5)(3x«  ~  5).  35.  (a  -  c)(a  +  26).  36.  c^{c^  -  6)(c8  +  6c» 
+  36).  37.  (a  +  26  —  c)(a  -  26  +  c).  38.  (a  —  m  +  n)(a  —  m  —  n). 
39.  3(x  -  a)(x  +  1).  40.  (7c  +  13) (c  +  1).  41.  (e  +  Sf)(e^  -  Sef 
+  64/2).  42.  (62/  -  7z){y  +  82).  43.  (a  -  66  +  t)(a  -  66  -  0- 
44.  (1  +  3x  +  52/)(l  -  3x  -  5y).  45.  (9c2  -  7d'Kc  +  d)(c  -  d). 
46.  (3m  +  2»)(3m  -  2n){7:i  +  n)(m  -  n).  47.  (a  +  6)(a  -  6  -  1). 
48.  (a  +  6)(a2  -  a6  +  62  +  a  -  6).  49.  (2a  -  6  +  3c  +  4d)(2a  -  6  - 
3c  -  M).  50.  (x  +  2/  -  3)(x  +  2/  -  2).  51.  ax2/(a2  +  62) (a  +  6)(a  - 
6).  52.  x'»(2x2»  4.  i)(2x2»  -  1).  53.  (7a*  -  66v)2.  54.  (25x3  -  SQy^) 
(x  -  y){x^  +  X2/  +  ^2).  55.  (x2  +  Qy^){x'  -  9x'y*  +  81^^. 
56.  [Ur^iy  -  z)  +  15s]  [14r3(2/  -  z)  -  15s].  57.  (2x  +  2/  +  1)^.  58. 
(3c  -  2e  -  5)(d  +  7).     59.  (x2  +  2/2  -  2)(x  +  y)ix  -  2/).    60.  (72/  -  5z)K 

Page  106.— 1.  ±5.  2.  ±  6.  3.  0,  4.  4.  0,  a.  5.  5,  2.  6.  5,  -  2. 
7.  0,  7.  8.  0,  3.  9.  -  9,  8.  10.  a,  a.  11.  0,  V2.  12.  0,  a/6.  13.  dt  a. 
14.  V2,2.     15.   -V4,V3.     16.  V6,V6.     17.2/5,3/6.     18.  a,  6.     19.  0,  a  +  6. 

20.  c/3,  a/2.      21.  0,  2,  -  2.      22.  2,  2,  -  2.     23.  0,  2,  1,     24.  0,  4,  5. 
Pages  107-110.— 1.  -  7,  6.      2.  7,   -  2.      3.  -  11,  10.      4.  29,  11. 


10  ANSWERS. 

5.  -  8,  -  5;  6,  8.  7.  6  ft.  8.  3  in.  9.  7  persons;  $12.  10.  2a:  -fl; 
odd.  11.  6,  7;  -  7,  -  6.  12.  -  11,  -  9;  9, 11.  13.  8  seats.  14.  3  in. 
15.  10  ft.  less.  16,  8  in.  17.  6  in.  18.  12  ft.  19.  7  ft.,  10  ft. 
20.  9  ft.,  12  ft.,  15  ft.  21.  216  sq.  in.  22.  141.4  in.  23.  853V«  sq.  ft. 
24.  10ft.    25.  15 in.    26.  9ft.,  11  ft.,  12ft.    27.  14 in.    28.  2828^7 sq.ft. 

Page    111.— 1.  6o«  -f  5a«  -  19a*  +  13a  -  5.  2.  3a»  +  2a*  -  6a» 

+  5a«  -  14a  +  6.       3.  6x*  -f  7x»  -  10x«  +  17x  -  20.  4.  x*  -  y*. 

5.  4a:»  -  IQx'^y  +  l%xy^  -  ^y^,  6.  x*  +  a:*  +  1.  7.  1  -  3a  +  a*  +  3a» 
-  a*  -  2a^  +  a\  8.  c«  -  2c7  -f  c«  -  2c^  -f  4c*  -  2c»  +  c«  -  2c  +  1. 
9.  x«  -  yK  10.  -  18a«  +  21a5  -  11a*  +  5a»  +  3a«  -  o  +  1. 

11.  m8  +  3m5  -  11m*  -  15w»  +  50w2  -  36m  +  8.  12.  15r^  -  f^  + 
35r*  -  9r»  +  21r»  +  2r  -  7.  13.  a^  -  68.  14.  x»  -  Zxyz  +  2/»  +  «». 
15.  8a:8  4.  i0a;6  ..  63a;*  +  27x«  +  49a;*  -  37x  +  6. 

Page  113.— 1.  x2  -  7a;  +  2.     2.  2a2  +  3a6  +  46*.    3.  2a*  +  5o6  -  36«. 

4.  x*  -  a;  +  3.  5.  a  -  6.  6.  5a*  -  2a  +  1.  7.  r^  ^' r^  -  1. 

8.  a*  +  06  +  6*.  9.  X*  +  x^y  +  a;*2/*  -f  xj/'  -f  2/*-  10.  a*  -  06  -  oc 
+  6*  -  6c  +  c*.  11.  x'  +  3x*  +  4x  +  2.  12.  x*  -f  x»2/  +  xy^  -f  |/«. 
13.  a»  +  2a*6  +  2a62  +  6^        14.  a^  -  a*6  -  06*  +  6*.        15.  2y, 

Pages  115-116.-1.  a*  -  2a  +  1.  2.  x*  -  3x  +  2.  3.  c»  -f  3c*  -  4c  -  1. 

4.  2x*  -  3x*  -  6.  5.  5x3  _  2x^y  +  3x2/*  -  22/*.  6.  3c*d  -  3cd*  -  2dK 
7.  mW  -  3mwr  -  4r2.  8.  x*  -  x/3.  9.  a/2  -  6/3  + 1.  10. 

2x  -  5  +  l/2x. 

r  Pages  117-118.-1.  57.  2.  78.  3.  227.  4.  306.         5.  498. 

6.  10.87.        7.  1005.        8.  3.24.        9.  .0751.         10.  8.01.         11.  .1234. 

12.  38.2.  13.  20.506.  14.  2784.53.  15.  1.414.  16.  1.732.  17.  2.236. 
18.  .816.       19.  .894.       20.  .942. 

Pages  122-123.— 1.  11.32  fr.      2.  16.98  fr.      3.  33.96  fr.      4.  31.13  fr. 

5.  25.47  fr.  6.  19.81  fr.  7.  $.883.  8.  $1.76.  9.  $2.64.  10.  $3.52. 
11.  $4.41.       12.  $4.76. 

Page  127.-1.  7,  5.      2.  1,  -  3.      3.  20,  10.      4.  IVs,  l*/8.      5.  Vj,  V4. 

6.  0,  2.  7.  Infinite  no.  of  roots.  8.  3, 2.  9.  Inconsistent.  10.  12, 13. 
11.  -4,-7.       12.  -  8,  13. 

Page  128.-1.  0,  2.       2.  12,  12.       3.  6,  20.       4.  15,  1.       5.  23,  -  1. 
6.  -  3,  4.         7.  V4,  -  Ve.         8.  13,  2.         9.  V«,  1.         10-  -  1,  -  V2. 

11.  Infinite  no.  of  roots.      12.  Inconsistent. 

Page  129.— 1.  1,  2.        2.  8,  9. 
6.  0,  -  V4.       7.  5,  1.       8.  34,  15. 

12.  7,  -  2.       13.  +  6,  +  3.       14. 


3.  13,  25. 

4.  V4,  2. 

5.  14,  6. 

9.  14,  8. 

10.  16,  23. 

11.  10,  6. 

-  20,  -  30. 

ANSWERS.  11 

P«e.  131-132.-1.  --±-\  -^^  2.  ^^  Lr^. 

3    £^_dbj^    en  —  dm         .      ahcd  bed  «     d  -h  n         c  —  m 

'  o5  +  (i '  a6  4-  d  '        '  dm  -^  en'  en  -^  dm' 
b  —  a     —  b  —  a 

2c  +  3d    2d  -3c  oc  +  ad    be-bd 

~135~  •      "•        2~~  •       2      • 
,.   et(bm  —  aw)    ab(o>n  —  hn)  ,_     e 

**•       6«-o»      '       o«  -  6«      •  "•  2x  • 

2^  18.  f.^.  19.^. 


.    AC    3608 
^**  360 '    C    • 

2.  2,  2.      3.  Vi,  -  Vi.      4.  »A,  Va. 

o  4-c  y   3m  -h2n     3m  -f  2n 

5  -I-  d*  6c  -  ad  •  ^'  5m  +  an'   26  -  3a  • 

9   1    ^        10   1    L 

9a'  56  n'  m 

Pages  134-135.— 1.  37?,  0, 37?.     2.  7,  -  7, 2.     3.  Infinite  no.  of  roots. 

4.  5,  5,  5.     5.  3,  -  2,  -  2Vj.     6.  3,  -  2,  6.     7.  4, 1,  -  2.     8.  15, 10, 12. 

9.  1,  Va,  V«.      10.   --  V8,  V2,  1.      11.  V37,  -  Ve,  -  Vm.      12.  .1,  .2,  .5,  .3. 

Pages  135-138.— 1.  41,  37.      2.  51,  25.      3.  28V2,  I6V2.     4.  9Vi,  15V». 

5.  12,  11.        6.  25,  47.        7.  -  44,  -  54.        8.  14,  12.        9.  $85,  $40. 

10.  $5750,  $5500.  11,  46  yrs.,  25  yrs.  12.  30c,  6c.  13.  $1.25,  30c. 
14.  27,  16.  15.  Vs.  16.  6,  15,  8.  17.  $1,  $1.50,  $1.75.  18.  35,  22. 
19.  $20.  20.  A,  $25;  B  $75.  21.  V/i  days.  22.  A,  5V7  days;  B,  13Vi. 
days;  C  40  days.  23.  15  boys;  $4;  $60.  24.  45.  25.  Any  number 
in  which  the  tens'  digit  exceeds  the  units'  digit  by  5.  26.  236.  27.  A  to 
B,  50  mi. ;  B  to  C,  90  mi. ;  C  to  A,  60  mi.  28.  15  mi.,  12  in.  29.  10  hrs., 
50  mi.  per  hr.,  500  mi.  30.  $5000  @  4% ;  $7000  @  3V2%.  31.  A,  $5000; 
B,  $3750.      32.  $1050.      33.  88c;  28c. 

Page  142.— 1.  ±  Vj  V5.  3.  rb  2.     4.  =b  VS.     5.  ±  V2.  6.  ±  Vlo! 

7.  ±  V6.           8.  ±3.  9.  d:2V2'.            10.  ±  V16.  11.  ±3. 

12.  0,  -  2.89.  13.  0, 1.5.  14.  ±  «/«.  15.  ±  7*^55.  16.  ±  V.15. 
17.  0,  8. 


12  ANSWERS. 

Pages  144-147.— 1.  2,  -  8.    2.  2,  -  12.     3.  •/»,  -  '/a-  4-  'A,  -  'A. 

S.  v..  -  V,.     6.  3,  -  'A.    8.  -  V.  ±  VIO.    9.  2^.  10.  2^5. 

11.  5  ±2^        12.  ~^^^.  13.  V:o.  -  »V...  14.  ^^• 

15,  Vn,  -  Vu.      16.  'A,  -  2.      17.  0,  «A.       18.  0,  -  2.  19.  ^  =^  "^^^ 


4 


M    6/  ^.jr       „     -7±  Vi049          „   6d:>S8i           „    1±_^. 
20.  Vii  V5.       21. g^ .       22. 22 •        23.  g 

24.  I±^^.      25.  v.. -v..     26.^1-=|^.     27.  -7±V^.  . 

28.  i^^.     29.  ::iif^.     30.  -^t^.      31.2±>i: 

—  4  o  10 

32.V,.-1.       33.  'A.   "A.         34.  Zil^:^.       35.   "  ^'^  ^^"^. 

D  4 

36.3^.         37.i*3^.         38.  -V. 'A.         39.17.-27. 

40.1V,,  -v..          41.3^.         42.  «^^.  43.^-^. 

45.  ±3->S,   ±2a5,    ±2aV3,   ±  5a6V2,   ±  10x«a/35.  46.  2±2>S'. 

47.3±2V7.           48.^1:!!?.           49.?^.  SO.  ^^. 

51.  3  ±2^5:           53.  L^p^  .           54.  1,  -  Vs.  55.  L±^. 

56.  5,  -  4.        57.  =b  a/s:        58.  5,  Vs.      59.  9,  Vs.      60.  ""  ^  "^  f^^ ^ 
61.  ±  VlO.      62.  6,  2. 

Pages  147-150.— 2.  13,  11.  3.  16  in.,  7  in.  4.  ^Vs  in.,  Vs  in. 

5.  V2  ft.,  "/2  ft.  6.  3V2  ft.,  IOV2  ft.  7.  10  in.  sq.  8.  13  in.,  11  in. 
9.  2V2  ft.  10.  4  in.,  7  in.  11.  40  ft.,  50  ft.,  30  ft.  12.  6  +  3>/2  in., 
3  4-  3>/Jin.  13.  59,  60;  -  60,  -  59.  14.  11  in.,  16  in.  15.  27,  -  7- 
16.  44  books.  17.  28  days.  18.  2  in.  19.  5  in.,  9  in.,  4  in. 
20.  7  ft.,  27  ft.  21.  175,  176;  -  176,  -  175.  22.  32,  34;  -  34,  -  32.  . 
23.  27,  29;  -  29,  -  27.      24.  6  ft.,  9  ft.,  18  ft. 

T»-      iei      o    1    8/         o    -5:tVl30          .    ^        ,,      -    3  =t  2V6 
Page  151. — 2.  1,  Ve.       3.  = .       4.  2,  —  Vs.    5. = . 

7  o 

6.  5±^.       7.  i-^^.  8.  18±V354.  9.-5^2^7. 


10.1,  -Vs.      lL16d:2V55.      12.^Q^=^/^^ 


ANSWERS.  13 

Pages  151-152.— 1.  9,-2.  2.  3  ±  >ff7.  3.  -  16,  -  2. 

I/O            «    ~5=fc  V35             ^    --25^  Vi45  „   ^    . 

4.  -  Vj,  -  2.  5.  2 •  ^-  15 •  ^-  ^'  ^' 

8.  14,  -  10.         9.  3,  -  6.         10.  0,  -  7.         11.  6,  -IS.         12.  3,  2. 

13.  -  15,  3.        l4.-l-±^}^  .        15.  1/,.        16.  5,  3.         17.  2,  -  V*. 
V  18.  11.      10.  Va,  -  2.       20.  Vi8.      21.  V2,  Vs.       22.  Va-       23.  5,  -  "/t. 

24.  V6,  -  V2.  25.  1  ±  V2,  26.  '^  ^  ^         '  ^^'  =*=  '/'^• 

^  28    "^=^^        29   ^^^         30   ^^^. 

Page  153.— 1.  ""  ^  "t  ^^^  .         2.  -  1  d:  V=^.         3.  1  d=  2>P1. 


-3:i:  V~^ 

4  • 

Page  156.— 1.  1,  25;  2,  -  10.  2.  3,  «/»;  2,  -  "/,.        3.  10,  -  6; 

20,  "A.      4.  -  45,  10;  «V2,  10.  5.  Vs,  "/21;  1,   -  Vt.        6.  0,  -  Vs; 

0,  !«/•.      7.  -  3,  -  «A2;  3,  -  Vi.  8.  -  2,  -  "A;  3,  -  8.      9.  8,  4; 

3,  -  1.      10.  5,  1;  -  10,  -2. 

Page  157.— 2.  3,  -  "Ao;  30,  'sVio.      3.  Vs;  Va.      4.  30,  50. 

Pages  158-160.— 2.  12,  -  3;  -  3,  12.  3.  12,  11;  11,  12.  4.  V2,  Va; 
Va,  V2.  5.  I2V2,  -  IV2;  IV2,  -  I2V2.  6.  7,  -  6;  5,  -  8.  7.  -  6,  5. 
8.  V2,  -  V3;  -  Vs,  V2.  9.  3,  2.  11.  3,  -  2;  2,  -  3.  12.  -  Vs,  +  4; 
-  "A,  +  5.  13.  5,  -  "A;  2,  -  "A.  14.  »Vi3,  7;  "As,  8.  15.  -  15,  5; 
15,  5.         16.  1.  15;  3,  -  11.  17.  2,  6;  4,  0.         18.  13,  -  3;  18,  2. 

19.  10,  -  14;  11,  -  5.      20.  1,  Vis;  1,  -  "As.      21.  ^so/.^,  iQ;   -  7o/^,,  10. 
22.  "V26,  2;  -  *^U,  3.     23.  ±  11;  d=  11.     24.  ±  1;  =F  1.     25.  5,  -  9; 

4,  -  10.      26.  2,  -  8;  7,  13. 

Pages  162-163.-1.  No;  No.       3.  2".       5.  "/89.       6.  x/y.     7.  x/my. 

8.1.       9.^i^.        10.^4±i^.        11.  v..        12.?^^-^        13.?. 

X  —  y  2x{x  —  1)  X  y 

...-,.  .5.—,.  .,.1^;.  .7.||±|. 

,s,^+»L.    „.-.,,.    20..  +  ,.    21.1+5.    2j.e<!^:i). 

—  X  —  y  o  d 

23.-^.        24.  ?^^        25.?^.        2«.-^.        27.-5. 

jre  +  3  y  —  4  4  a  —  y 

28   ^        29         °  +  ^  30   JL^Z±-       31    y-2^        32    ^-TJ? 


14  ANSWERS. 

Pages  165-l«».-3.^.  4.  f  .  5.g'.  6.  5^>. 

7.2x(l-y).       8.1.       9.^^^'.       10.%.       11.  ^^' +  ^  +  ^>  . 
,2.V.  13.''^^'-^  +  ^'>.  14.4(x-j,).  15.Wl£>. 

16   ?        17  'g  18  3a;»  12x  +  y 

» '  2j/(l  -2x+  4x«)  •      *"•  j/»(l  +3y  +  9y^)  *      *"•    »  +  j,    • 

20.    .^^  +  ^     ,.        21.(2x  +  3)..       22.-f±|,.       23.  <^1^ . 
x^  -{-xy  —  y^  x(x  4-5)  x*  ^ 

24.  (x  +  yKx  -  l)(x2  -  X  +  1). 
Page  167.--^   14^:^^  ^   m«  -  n«  ^    m  4- 1 


72/  +  5a;  *  *  m*  +  n»  *  2w  -  1  * 

^•I2(4mn+l)-         «'  "^  •         '•"/'•         ^»-  "/'"         "' t^-a  • 

g«  +  a;  -  4        -.   2  4-1/  -g 

lib*  r  =         •  X<9*  ,  • 

a;*  —  7  X  -{-  y 

Pages  168-169.-1.  a*.     2.  xj/.     3.  5a*.     4.  6a'^bc.     5.  o.     6.  a;  —  |/. 

7.  a;«  4-  2/*.  8.  a  4-  &.  9.  x  -  y,  10.  a;  -  1.  11.  2(a  4-  1). 
12.  a  4-  &.  13.  X  -  y,  14.  x  -  2.  15.  a;  4-  2/.  16.  m  4-  3. 
17.  a  -  1.           18.  o2(a  4-  2).          19.  (x  4-  yy(x  -  2/)^  20.  r  -  2s. 

Pages  169-170.— 1.  xyz,  2.  a^hK  3.  fe'c^d*.  4.  70  cde. 

5.  a*(a  4-  1).     6.  a{a  4-  l)(a  -  1).     7.  cd(c  +  <i).     8.  ab(a  4-  6) (a  -  6). 

9.  (a  4-  2)(a  ~  2)(a  4-  3).  10.  (x  ~  2/)Ha;  4-  2/)'.  11.  (a  -  b^ia  4- 
6)(a*  +  o&  4-  fe^).  12.  (m  4-  n)2(w2  4-  n*).  13.  3(w  -  w)(m»  4-  nm 
4-  n«).  14.  (x  4-  2)(x  4-  3)^  15.  (a  ~  4)(a  -  2) (a  4-  3).  16.  (1  4- 
x)(l-x)(14-a;4-a;*).  17.  x2/2(x4-2/)(a:  -  2/).  18.  (x -3)(x4-3)(x4- 7). 
19.  (a  4-  l)(a  -  l)(a2  4-  1).      20.  (x  -  2ynx  4-  42/) (x  4-  2/). 

Page  170.— 1.  12;  72.        2.  48;  288.        3.  49;  294.        4.  36;  7560. 
5.  2x2/;  40x62/»2«.  6.  25;  300ao»d^  7.  a;  3a(a  -  6). 

8.  4ax;  ^ax^a^  -  x«).  9.  x  4-  3;  (x  4-  3)(x  -  3)(x  4*  2). 

10.  6  4-  a;;  ab{b  +  x).  11.  x  4-  2/5  (^  +  2/)*(2J  —  y)i^^  —  xy  4-  2/*). 
12.  3  -  a;  4(3  ~  a)*(9  4-  3a  4-  a*).         13.  a  -  26;  a(a  -  26) (a  4-  36) (a     , 
-  46).      14.  c+d;  (c  4-  ci)(c  -  2d)(?n  -  n). 

Pages  171-172.-1.  -/..  2.  ?ii±A^  3.  452/+  25x  4-4 

,    10a*6  -  2a6«  4- 3a*6«  ^  x  +  3y  ^  x  -  82/ 


75       •  15xV 

f  32/  g  x-32/ 

50  •  "•       10     •  ^'  {x4-2/)(iC'-l/)' 

+  x-y  g  gi  4-  X2/  -  1  p^  y  ^^   1 

(x  -  2/)'   *  *      (x  4-  2/)'     '  '  («  4-  2/)(ic  -  1/)  *  '  ^' 


ANSWERS.  15 

11    5x«  ->  2xv  -f  5y«                             2x  2y 

6(x  +  y)(x  -  2/)  •          "•  (X  +  yKx  -  y) '  ^^*  (x  +  y)(x-y)* 

14.  -^-±^.                   15.  --i:2x^+J^.  16,          31 


a;(m  -  x)  •  *  x(x  +  y)(a;  -  j/)  *  12(2a;  +  6) 

!y  -  1)  • 

2o  +  26  +  2c 
(a  +  6)(6  +  c)(a  +  c)^ 


17        y  +  ^  18    i2£jLl  ig         ^  20    0 

^^•30(3y~l)-  ^®-35(x4.1)-  ^^- sT     ^'  ^^- ^' 

21. 


Pages  173-174.— 1.  IVt.      2.  3V«.      3.  P/s.      4.  5.      5.  V/v.      6.  6. 

/«.       12.  V7. 
33  db  V409 


7.  IVw.      8.      ^        .      9.  0,  9.      10.  -  IV26.       11.  -  "/m.       12.  V7. 


13.  1.     14.  IVe.      15.   -  5.      16.  0,  -  V2.      17.  3,  V3.      18. 

19.  IVfi.  20.  3,  -  7.  21.  -  4  rfc  V5.  22.  0,  5.  23.  6,  -  3. 
24.  2,  -  1.         25.  -  6,  -  6.         26.  2,  2.         27.  11,  "A*.         28.  IVj. 

29.  ^2V.      30.1^. 

Pages  174-176.— 1.  -  12,  6.         2.  182.         3.  17  yrs.         4.  30  yrs. 

5.  V».        6.  16  in.  by  12  in.        7.  4  in.  by  6  in.        8.  35,  49.        9.  120. 

10.  40  mi.,  50  mi.       11.  4  hrs.       12.  S^h  hrs.       13.  13Vs  hrs.       14.  24. 

15.  6000  tons.     16.  $12,000.     17.  5V2yrs.     18.  6  games.     19.  160  cu.  ft. 

Page  181.-1.  ^aT         2.  V5«.         3.  ^xV-         4.  V7a.         5.  2^5x. 

6.  2\^a2.  7.  ^4a2.  S.2<x^ly,  9.6^la^^ly.  10.  7^(3m)«I 

11.  Va6.     12.  3^5.     13.  <lix  +  y)\    14.  4\'(c  ~  d)«.    IS.  S^o^Vx^. 

16.  a*\^6^. 

Pages  182-183.— 1.  V«.      2.  8.     3.  5.     4.  V2.     5.  27.     6.  9.     7.  5. 
8.  V4.    9.  42.     10.  -  1V4.     11.  9.     12.  V,.     13.  -  'A-     14.  V».     15.  V«. 

16.  Vs.        17.  25.        18.  Vt.        19.  9.        20.  1.        21.  |.      '  22.  l2yK 

23.6X2,'..      24.  -|i.      25.?4-\      26.  ^t^ . 
16a2  o5  6  —  a 

Pages  184-185.— 1.  2V2.       2.  2^3^       3.  2V5^       4.  2V6;        5.  2V7l 
6.  2VIO.       7.  6Vri.      8.  12^.      9.  -  ISVS*.       10.  20V3;       11.  2Vl4. 

12.  77.         13.  -32ViO.  14.  10  VS^  15.  15  Vs!  16.  -OOVsI 

17.  271/2.  18.  16V5^  19.  -2V3*.  20.  w/sVs".  21.  2\^2; 
22.  6^2.  23.  10\'2'.  24.  14^^71  25.  6^11.  26.  3^2l 
27.  100^10.      28.  2.^  29.  6<ls,       30.  14^10.       31.  2\^7".        32.  x<x. 


16  ANSWERS. 

33.  c^-^c,  34.  y'-^.  35.  ac^.           36.  hx^ly.  37.  ir^4nm, 

38.  VaA/a;  39.  VsVS".  40.  V4Vi4.           41.  Ve^^.           42.  V«>/3l 

43.  Ve^.  44.  VwVs".  45.  Vs^^lS.       46.  V2^T;  47.  ^U^%      48.  ^6: 

4P.  Vf^ii.  50.  V8^45.  51.  Vi.       52.  ^aS".  53.  -V^       54.  ^Vl 

55.  —r—^xTy.  56.  -\'^.  57.  Va;'  -  y*. 

ic  +  y  2/ 


m^n     i— ; .  _,^       1        I £ 


58.  <m{m  —  n).  59.  r  Va  —  6.  60.  {x  +  2/)  Vx^  y. 

m  —  n  a  —  o 

Page  186.— 1.  -  ^  2.  7^5:      3.  SVu.      4.  7<a.      5.  (a  +  &)>/&: 

6.  V2^.          7.  8^.  8.  V2V6.         9.   -  VibVIS.          10.  ^^  V5. 

11.  4>/5'.         12.  14 aS;  13.  I5V7:         14.  0.         15.  (a  +  6  -  Z)<b. 
16.  (2a-c4-2J>/a6.  17.  ^'"^^"^  ■■Vi.          18.  (a  +  5)  VSTT - 

Va«  -  6«.  19.  ^^  +  ^  -  ^  V^.  20.  (x  -  y  -  2a;y)  VJ+T- 

mn 

21.  9^2.     22.  ^iM-  W,     23.  5\'x"^=^.     24.  i^JcT^. 

Pages  187-188.— 1.  3  aS"  -  V2T  -  2  >/§!  2.  V35  +  Vl5  -  V55. 

3.  6V3~-  6^l2  +  V30.  4.  5^  -  8 V5  +  10.  5.  -  27 V2  +  42. 

6.  21  +  7->S  -  3>/3  -  VeT  7.  8^5  -  V30  -  32  +  4V6: 

8.  -  48  -  7V5.  9.  -  70.  10.  30.  11.  -  5  +  2^42. 

12.  10>S  -  6VT5  -  4V70  -  10  +  3V3O  +  4V35  -  2V1O  +  6V3  +  4Vi4". 

13.  3  4-  "/3o>/30  -  1735 >/35  -  iV42>/42.        14.  {x  -y)^xy+x^  +  y<x. 
15.  -  3  -  ^^12  +  2\'2  +  a'IS  +  ^36  -  ^4  -  \^6. 

Page  189.-1.  VsVlO.         2.  Vs^.         3.  4>/6.        4.  ^4.        5.  3V3. 

6.  12-f6V3.  7.^^^.  8.^^^^'.  9.^%-^ 

0  +  6  X  —  y  4 

^p  21  +  12 V7  U.  -V10-VI5+2V3  +  3V2. 

-^    yg-f Vi0  4-3>S4-^  ,,    -^-V6  +  5>S-ViO 

\£.  3^|j  13.  ^^^"2  . 

14.  -5'J3+Vl5+3Vl0 -3V2.  15.  -23  +  4^. 
ie.35±^                    17.  -5  +  2V§.                   18.?L±|^. 

o  +  &  *         *  y 


ANSWERS.  17 

Page  191.— 1.  9.  2.  "/o.  3.  -  1.  4.  11.  5.  2Vj.  6.  "/»•  7.  6. 
8.  2.     9.  7.     10.  1.     11.  3.     12.  V26.     13.  8.     14.  -6.     15.  3.     16.  7. 

Page  192.— 1.  -  5.  2.  16.  3.  8.  4.  3a  +  c. 

5.  -  Sx^  -  ISy''  ,-f-  X  +I3y,       6.  V  -  2x2/.       7.  -  a  +  26  -  2c  -  3d. 

8.  -  3a  +  26  -  c  +  d.  9.  (a  -  6  +  4c)  -  (a6  -  2ac  +  46c  -  a26). 
10.  (-  a;  +  6y  -  4z)  -  {-  xy  +  Sxz  -  7yz).  11.  (2a;'  -  5y^  +  32*)  - 
(2x2  -  2yz  -  4a;y).     12.  (f  -  d  +  2c  -  3e)  -  (4cd  +  3de)  +  cde. 

Page  193.— 1.  x^  +  1.  2.  4<2  +  8<  +  1.  3.  4^2  4.  1,  4,  _  4^,2  _  1^ 
5.  x2  +  2xy  +  2/2.  6.  m^  -  8m.  7.  a;  +  5y.  8.  2a;2  +  2y\ 

9.  2a2  -  4a6  +  262.         10.  2a2  -  2a6  -  6^.         11.  64,  81,  4,  1,  1,  1,  5. 

12.  aS  a«,  4c7,  x^,  2/10.      13.  a'^,  6-',  VsC'S  x',  x'^.      14.  ^' ,  30^62,  ^ ,  -^  . 

oa  5     xy 

15.  2a2  4-  262.  15.  2a2  -  2a6  +  562.  17.  ^2  +  2a6  -  4ac  +  62 

-  46c  +  4c2.  18.  4a6  +  562.  19.  ^a^  ^  6ab  +  262.  20.  -  2a6  +  562. 
29.  2/2  +  2/  -  2.  30.  2/^  -  62/  +  57.  31.  4x2  +  3x  +  2  + 

16x2  _  25x  -  22 
x'  -  2x2  4.  6a.  _{_  5* 

Page  194.— 1.  5xy\2  -  3x).  2.  (2x  +  y){a  +  6).  3.  2x(a  +  6). 
4.  x'(x  +  l)(x2  -  6x  +  3).  5.  x3(x2  +  l)(x  -  5).  6.  (a  -  6)2(a  +  6). 
7.  (m  +  n)(x  +  l)(x  ~  1).     8.  (3x2  4.  i)(a.  _  i)^     9.  (3^  _  2n)(a2+62). 

10.  (m  -  n)(m  -  n  -  1).       11.  (a  +  y)(h  -  x).       12.  (a2  -f  62)(a  -  6). 

13.  (2/  +  5)2.  14.  (x  +  4)2.  15.  (06  +  6)2.  16.  (a  -  6  -  c)2. 
17.  (m  -f  7)(m  -  7).  18.  (8  +  x)(8  -  x).  19.  (9x2  4.  5yZ)(gx^  -  5yi), 
20.  (a  -  6  +  c)(a  -  6  -  c).  21.  (6x  +  2/)(-  4x  -  y).  22.  (a  +  6 
+  c)(a  4-  6  -  c).  23.  (x  -  4)(x  -  1).  24.  (x  +  4)(x  +  1). 
25.  (2/  +  8)(2/  -  2).  26.  (y  -  8)(y  +  2).  27.  (x  -  2)(x  -  5). 
28.  (x  +  2)(x  4-  5).  29.  (x  +  5)(x  -  2).  30.  (x  -  5)(x  +  2). 
31.  (a  +  9)(a  -  2).  32.  (6  -  15)(6  +  3).  33.  (c  +  16)(c  -  2). 
34.  (x  +  15) (x  -  5).  35.  (x  -  15) (x  -f  5).  36.  (x  -  Sy)(x  +  y). 
37.  x2(l  -f  142/)(1  +  2/).  38.  (10a  +  l)(7a  +  1).  39.  (2x  4-  3)(x  +  3). 
40.  (2  +  32/)(l  -  22/).  41.  (3  -  5m)(2  +  3m).  42.  (a  4-  26)(a2  - 
2a6  4-  462).  43.  ^a  -  26)(a2  +  2a6  4-  462).  44.  (^^  -  Sy)i4x^  4-  6x2/ 
4-  92/2).      45.  (2x  +  32/)(4x2  -  Qxy  +  91/2).      45.  ^^2  4.  i)(^  4.  i)(a.  _  i). 

Pages  195-196.-5.  2.      6.  ^1^.      7.7.      8.^.      9.^^. 

10.--^.        11.-^5-.        12.7^2.        13.^,.        14.  ^^i. 
n(a  -  6)  X  -  y  (x  -  2)2  2xy^  y 

15.  ^^-qr^  .        10.      5      .        17.  ^,  ^  3^  ^  Q .        18.  ^2  __  ^, . 

-2m2  ^^      /  X  ^,    a2+26  „    x-2 

l^'  —T-t i — i-  20.  a(a  -  x).  21.     ^T_  .    .  22. ^  . 

m2-|-mn  +  n2  a  +  6  x  —  7 


18  ANSWERS. 

o«  24y  (x  —  y)»  (*  —  1)»  • 

27  5^-y  28  -°  29    iJ"-^ 

"'  (x  -  y)(x  +  y)  •  '*"•  (a  -  3)(a  -  4)  '  -«»•       4       ■ 

30.?i±il^.      31.?^±^.      32.^^'.      33.^-.     34,      "' 


Pages  196-197.— 1.  Vis.       2.  1.       3.  10.       4.  -  »/«.       5.  -  "/e.. 
^  IV,.       7.  -^—.       8.  -4-i:.        9.  ?-±^.        10.        '^ 


11.      ^"^^  ;.        12.^-^.       13.-7.       14.  »/«.       15.1.       16.3. 

17.  2Vi.      18.  Va.      19.  -  Ve.     20.  1.     21.  No  root.     22.  "/a.     23.  4. 
24.  5.     25.  -  "/«.     26.  "A,  "A-     27.  "/i.  19.     28.  2,  5.     29.  2V2,  2Vi. 

30.  6,  5.      31.  1,  1.      ""   ^^' 


32. 

3 

,  c. 

5,1. 

2    ^^ 
^'        2 

J 

6. 

-  v.,  - 

v.. 

Pages  197-198.— 1.  5,  1.         2.  "  "t  ^" .         3.  4,   1.         4.  3,    -  */». 


5.  9,    -  «/».  6.  --  Vj,   -  Vj.  7.  o  d:  Va»  4-  6^ 


8    (•* 

-  1)  ±  Vo» 

-6a  +  l 

2 

in    "" 

•  «  ±  V?«  - 

4pr 

AU. 

2p 

* 

„    -  m  ±  Vm»  -  4j» 
'•                2 

..  -  Vf,  2. 

12.  v.,  v..           13.  5,  v.. 

14.  =b  Vi.  15.  d=  VcSTl.  16.  «A,  3.  17.  d:  6,  d=  9.  18.  ±  6,  d:  4. 
19.  -  »/6,  1.  20.  25,  9;  -  10,  6.  21.  V»,  Va.  22.  Vi,  2.  23.  d=  4,  ±  3. 
24.  0,  8;  0,  4. 

Pages  198-200.— 1.  21.  2.  6  hrs.;  50  mi.  per  hr.  3.  13  ft.,  10  fU 
4.  150  cows.  5.  13  hrs.  6.  50  in.,  37  in.  7.  12doz.  8.  a  =  .2,  6  =  1.1, 
P  =  36.18.  9.  Mule  7  m. ;  donkey  5  m.  10.  10  ft.  11.  400  ft.  by  300  ft. 
12.  15  mi.  up,  12  mi.  down.  13.  $35.  14.  735  lbs.  15.  4Vii  gal. 
16.  $416. 

Pages  200-201.-2.  7,  500  lbs.  3.  45V4  lbs.  4.  IVm  ft.  5.  53V7  in. 
6.  128"/8»;  83"/8».  7.  3910  lbs.  8.  .04  -f  in.  9.  IVu  ft.  from  heavier 
end.      10.  VVu  ft. 

Page  202.— 5.  402.5  ft.      6.  253.7  ft.  per  sec.      7.  About  1247  ft. 


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